Question

in a TRIANGLE ABC
 ANGLE A= X
ANGLE B=3X-2
ANGLE C=Y

ALSO ANGLE C - ANGLE B=9
FIND THREE ANGLES OF TRIANGLE ABC

Answer 1

<A + <B + <C = 180
x + 3x - 2 + y = 180
4x + y = 182 -----------------------(1)
<C - <B = 9
y - 3x + 2 = 9
-3x + y = 7 -------------(2)
(1) - (2)
7x = 175
x = 25
y = 82
hence,
<A = 25
<B = 73
<C = 82

Answer 2

 angle A=X, angle B=3X-2, angle C=Y (Given)
Since it is given,
 angleC-angleB
⇒Y-(3X-2)=9
⇒Y-3X+2=9
We can find out the value of Y from the above formed equation,
⇒Y-3X=9-2
⇒Y=7+3X······························ (i)

Since we know all the angles of the triangles sum up to 180,
We can form the equation
angleA+angleB+angleC=180
Now substituting the values of the angles,
We get,
⇒X+3X-2+Y=180
We can replace the value of Y from equation (i),
we get,
⇒X+3X-2+7+3X=180
⇒7X+5=180
⇒7X=180-5
⇒X=175/7
⇒X=25

Since we got the value of X we can find out the values of other angles,

angle A= X  =25

angle B= 3X-2  =3*25-2 =73

angle C= Y =(7X+3) = 82

Hence, the angles are
angle A=25, angle B=73, angle C=82